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GrMatchingField -- the class of Grassmannian matching fields

Description

Common ways to define Grassmannian matching fields:

Two Grassmannian matching fields are said to be equal if and only if their tuples are the same.

Technical details. A Grassmannian matching field is derived from the class HashTable. All Grassmannian matching fields have the following fields:

  • k of type ZZ
  • n of type ZZ
  • tuples of type List, accessible withgetTuples
  • cache

Everything else, including: weight matrices; polynomial rings, maps and ideals; polyhedra such as the weight matrix cone and matching field polytope, are all stored inside the cache. Note that the package does not export the keys, such as k or n. If you wish to directly address the contents of the GrMatchingField, then use "debug MatchingFields".

See also

Menu

Functions and methods returning an object of class GrMatchingField:

  • grMatchingField -- Construct a matching field for the Grassmannian variety

Methods that use an object of class GrMatchingField:

  • algebraicMatroid(GrMatchingField) -- see algebraicMatroid -- The algebraic matroid of the tropical cone that induces the matroid
  • algebraicMatroidBases(GrMatchingField) -- see algebraicMatroidBases -- The bases of the algebraic matroid
  • algebraicMatroidCircuits(GrMatchingField) -- see algebraicMatroidCircuits -- The bases of the algebraic matroid
  • amalgamation(ZZ,GrMatchingField) -- see amalgamation -- The $i$th amalgamation of a tope field
  • getTuples(GrMatchingField) -- see getTuples -- The tuples of a matching field
  • getWeightMatrix(GrMatchingField) -- see getWeightMatrix -- weight matrix that induces the matching field
  • getWeightPluecker(GrMatchingField) -- see getWeightPluecker -- weight of the Pluecker variables induced by the weight matrix
  • GrMatchingField == GrMatchingField -- equality of Grassmannian matching fields
  • isCoherent(GrMatchingField) -- see isCoherent -- Is the matching field coherent
  • isLinkage(GrMatchingField) -- see isLinkage -- Test if a tope field is linkage
  • isToricDegeneration(GrMatchingField) -- see isToricDegeneration -- Does the matching field give rise to a toric degeneration
  • linearSpanTropCone(GrMatchingField) -- see linearSpanTropCone -- linear span of the tropical cone associated to the matching field
  • matchingFieldIdeal(GrMatchingField) -- see matchingFieldIdeal -- The toric ideal of a matching field
  • matchingFieldPolytope(GrMatchingField) -- see matchingFieldPolytope -- The polytope of a matching field
  • matchingFieldRingMap(GrMatchingField) -- see matchingFieldRingMap -- monomial map of the matching field
  • matroidSubdivision(GrMatchingField) -- see matroidSubdivision -- The matroid subdivision induced by the Pluecker weight of a coherent matching field
  • net(GrMatchingField) -- display a matching field
  • NOBody(GrMatchingField) -- see NOBody -- Newton-Okounkov body of the matching field
  • plueckerAlgebra(GrMatchingField) -- see plueckerAlgebra -- Pluecker algebra of a (partial) flag variety
  • Grassmannian(GrMatchingField) -- see plueckerIdeal -- The Pluecker ideal of a matching field
  • plueckerIdeal(GrMatchingField) -- see plueckerIdeal -- The Pluecker ideal of a matching field
  • plueckerMap(GrMatchingField) -- see plueckerMap -- The ring map of the Pluecker embedding
  • topeField(GrMatchingField) -- see topeField -- Constructor of a tope field
  • topeField(GrMatchingField,List) -- see topeField -- Constructor of a tope field
  • weightMatrixCone(GrMatchingField) -- see weightMatrixCone -- The cone of weight matrices that induce the matching field

For the programmer

The object GrMatchingField is a type, with ancestor classes HashTable < Thing.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/MatchingFields.m2:2337:0.